In many areas of research, such as within medical statistics, biology and geostatistics, problems arise requiring the analysis of angular (or directional) data. Many possess experimental design problems and require analysis of variance techniques for suitable analysis of the angular data. These techniques have been developed for very limited cases and the sensitivity of such techniques to the violation of assumptions made, and their possible extension to larger experimental models, has yet to be investigated. The general aim of this project is therefore to develop suitable experimental design models and analysis of variance type techniques for the analysis of directional data. Initially a generalised linear modelling approach is used to derive parameter estimates for one-way classification designs leading to maximum likelihood methods. This approach however, when applied to larger experimental designs is shown to be intractable due to optimization problems. The limited analysis of variance techniques presently available for angular data are reviewed and extended to take account of the possible addition of further factors within an experimental design. These are shown to breakdown under varying conditions and question basic underlying assumptions regarding the components within the original approach. A new analysis of variance approach is developed which possesses many desirable properties held in standard 'linear' statistical analysis of variance. Finally several data sets are analysed to support the validity of the new techniques.